The description of a mathematical model for the flash melting of Cu-concentrates

Abstract

In the present paper an attempt has been made to mathematically describe mass, momentum, and energy transfer in a turbulent flash melting reactor. The model is based on a separated two component flow with the assumption that although the solid concentration in the suspension is high its volume fraction is small. It has been further assumed that each particle causes a small force vector into the gas phase, and according to the principle of action and reaction, the gas phase influences the particle with a force vector equal in magnitude but opposite in sign [3]. Because there is net mass transfer over the phase boundary, the gas phase has a continuous mass source, which must also be considered. The turbulent mixing has been assumed to be proportional to the time mean gradient of concentration. The apparent turbulent diffusion coefficient has been assumed to be proportional to the square root of time mean turbulent kinetic energy, the proportionality factor being defined as turbulent mixing length in accordance with Prandtl and Kolmogoroff. For the turbulent kinetic energy, a balance equation has been derived with the assumption that turbulent kinetic energy is transported through convection and turbulent diffusion [1]. It has been further assumed that turbulent energy is created by the loss of mechanical energy of time mean velocities of the gas ([9] p. 110). The dissipation of turbulent energy takes place in the boundary layers of the particles and through the velocity gradients of small eddies. Particle reaction kinetics (particules/volume/time) has been described using the Arrhenius equation. Original concentrate particles first decompose thermally ( − CuFeS 2 + 1 2 Cu 2S + FeS + 1 4 S 2 = 0 , − FeS 2 + FeS + 1 2 S 2 = 0 ) producing gaseous S 2. After decomposition, combustion takes place. In the calculations four kinds of particles are considered: (1) initial concentrate particles, (2) thermally decomposed particles, (3) burned particles, and (4) inert particles (mainly SiO 2). Only one size fraction is assumed, and all transitions are assumed to be rapid and depend mainly on the local conditions. In the gas phase, only one reaction is considered ( − 1 2 S 2 − O 2 + SO 2 = 0 ). Balance equations are written for four gas components (O 2, S 2, SO 2, N 2). All together the developed model consisted of 18 partial differential equations, which were solved numerically with proper initial and boundary conditions.